PRP Records

Probable Primes Top 10000

(291192 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9751(17*10^88761-41)/388762Robert Price09/2017
9752(2^294834+2854)/288754Stefano Morozzi01/2020
9753(2^294823+2466)/288751Stefano Morozzi01/2020
9754(2^294764+642)/288733Stefano Morozzi01/2020
97552^294754+1501588730Lelio R Paula10/2013
9756(3^185951-7)/2088720Lelio R Paula01/2013
9757(2^294688+3186)/288710Stefano Morozzi01/2020
9758(2^294673+3906)/288706Stefano Morozzi01/2020
9759(2^294661+5)/44369338388694Lelio R Paula01/2013
9760(2^294631+2514)/288693Stefano Morozzi01/2020
9761(10^88680+11)/388680Robert Price11/2014
97622*7^104928-988675Lelio R Paula10/2014
976311^85150+1288675Lelio R Paula11/2015
97648*6^113951+588673Lelio R Paula10/2014
9765(2^294549+3110)/288668Stefano Morozzi01/2020
97666*10^88665-7988666Robert Price03/2022
97676^113940-1856388663Enzo Doria03/2013
976838^56123-56123^3888663Norbert Schneider02/2017
97692^294492-6588651Lelio R Paula10/2012
9770(2^294481+2822)/288648Stefano Morozzi01/2020
977123874^5165+5165^2387488646Hans Havermann08/2020
9772(2^294469+1466)/288644Stefano Morozzi01/2020
97737*10^88634-2788635Dylan Delgado08/2019
977420^68120-5388627Lelio R Paula01/2016
9775122^42477-12188623Norbert Schneider10/2018
97762^294391-11325788621Enzo Doria07/2014
97775^126784-1547688619Enzo Doria02/2013
9778(2^294335+554)/288604Stefano Morozzi01/2020
97792^294327+988602Lelio R Paula10/2012
97802^294320+1891588600Lelio R Paula10/2013
9781(98*10^88595-89)/9988595Ray Chandler07/2011
9782(5*10^88595+103)/988595Robert Price04/2022
978320723^18834+18834^2072388590Hans Havermann08/2020
9784(68*10^88586-329)/988587Robert Price03/2021
9785(2^294268+1402)/288584Stefano Morozzi01/2020
9786(17*2^294262-1)/1388582Lelio R Paula02/2014
97876*10^88571+7788572Robert Price06/2020
97882^294224-93307588571Paul Bourdelais04/2021
9789(2^294145+1346)/288547Stefano Morozzi01/2020
9790(2*10^88545+7)/988545Erik Branger03/2011
97912^294137-13388545Lelio R Paula10/2012
9792(2^294109+3494)/288536Stefano Morozzi01/2020
979323515^5818+5818^2351588529Hans Havermann08/2020
9794(2^294092-1017)/117188528Lelio R Paula01/2013
97954^147036+147036^4+188525Robert Price04/2014
979622541^8458+8458^2254188525Hans Havermann08/2020
9797(14^77213-5^77213)/988496Robert Price04/2013
97982^293965+279337788493Enzo Doria03/2016
9799(2^293956+3306)/288490Stefano Morozzi01/2020
980011^84971-15088489Enzo Doria08/2012
9801(2^293944+1066)/288486Stefano Morozzi01/2020
98029*10^88485+9188486Robert Price10/2020
980348^52626-4788478Norbert Schneider08/2018
9804(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
980511^84958-219088475Enzo Doria12/2012
9806(2^293902+3070)/288474Stefano Morozzi01/2020
9807(35*10^88471-89)/988472Robert Price02/2022
98082^293880-11134788467Enzo Doria05/2014
9809(106*10^88459-1)/388461Serge Batalov12/2014
981010^88457+27873388458Patrick De Geest07/2017
981110^88457-40188457Robert Price06/2017
9812(2^293834+3018)/288453Stefano Morozzi01/2020
9813(2^293747+1626)/288427Stefano Morozzi01/2020
981422080^10109+10109^2208088424Hans Havermann08/2020
981511^84908-168088423Enzo Doria12/2012
9816(2^293703+3486)/288414Stefano Morozzi01/2020
98172^293679-11207588407Enzo Doria06/2014
98186^113608-6588405Lelio R Paula12/2015
98192^293624+8287588390Lelio R Paula10/2013
9820(2^293618+918)/288388Stefano Morozzi01/2020
98212^293612-11233788387Enzo Doria06/2014
9822758^30693+30693^75888386Norbert Schneider05/2017
9823gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
98245*10^88377+7788378Robert Price06/2016
9825(2^293584+1558)/288378Stefano Morozzi01/2020
9826(5*2^293526+1)/30388359Lelio R Paula01/2013
982720918^16743+16743^2091888355Hans Havermann08/2020
9828(2^293499+2390)/288352Stefano Morozzi01/2020
982920727^18292+18292^2072788344Hans Havermann08/2020
98312^293461-278584388341Enzo Doria03/2016
9830(31*10^88340+257)/988341Robert Price12/2021
98332^293416-103788328Yves Minet11/2012
98326*10^88327+4388328Robert Price07/2020
9834(58*10^88321-49)/988322Robert Price05/2022
983525109^3292+3292^2510988320Hans Havermann08/2020
9836(2^293384-7)/388317Lelio R Paula01/2013
9837(3^185092-5)/488311Lelio R Paula01/2013
9838(5*10^88303-173)/388304Robert Price11/2017
983914^77039-5788297Lelio R Paula11/2015
98403*10^88293-5988294Robert Price10/2017
98415^126303+4288283Lelio R Paula10/2015
9842(88*10^88269+83)/988270Robert Price03/2022
984419^69025-1888266Theodore Burton01/2006
9843140^41128+13988266Norbert Schneider04/2019
98455*10^88261-388262Dmitry Domanov11/2010
9846(2^293195+2238)/288261Stefano Morozzi01/2020
98478^97731-7^(97731-1)88260Robert Price04/2016
98485*10^88254+5988255Robert Price09/2016
98494*3^184968-788253Lelio R Paula08/2014
985034*10^88251-988253Robert Price06/2020
98517^104426+8888251Lelio R Paula10/2015
98522^293142+9988245Lelio R Paula10/2012
985311^84736-213088244Enzo Doria12/2012
985423884^4945+4945^2388488232Hans Havermann08/2020
985522080^9907+9907^2208088231Hans Havermann08/2020
9856(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
98572^293068-8988223Lelio R Paula10/2012
98582126^26511+26511^212688218Norbert Schneider02/2020
98592^293014-10965588207Enzo Doria04/2014
98608*7^104371-388205Lelio R Paula10/2014
98612^292995-214588201Lelio R Paula10/2013
986228534^1233+1233^2853488198Hans Havermann08/2020
98635*10^88182+7788183Robert Price06/2016
98652^292929+4387788181Donovan Johnson04/2005
98646^113321+13188181Lelio R Paula12/2015
9866(2^292919+3366)/288178Stefano Morozzi01/2020
98672^292904-58394988173Paul Bourdelais04/2013
98682^292894-11185188170Enzo Doria05/2014
98692^292872-279734988164Enzo Doria03/2016
9870(2^292864+1042)/288161Stefano Morozzi01/2020
98712^292860-10968588160Enzo Doria04/2014
98729*6^113288-588157Lelio R Paula10/2014
9873(2^292735+2166)/288122Stefano Morozzi01/2020
9874(2^292735+2346)/288122Stefano Morozzi01/2020
9875(2^292705+1934)/288113Stefano Morozzi01/2020
9876(2*10^88112-23)/388112Robert Price09/2017
987729622^943+943^2962288111Hans Havermann08/2020
9878(73*10^88105+17)/988106Robert Price10/2015
9879(2^292673+3026)/288104Stefano Morozzi01/2020
988011^84588+7888090Lelio R Paula11/2015
9881(265*10^88077+11)/388079Robert Price03/2017
988291^44959-90^4495988077Robert Price07/2015
98836^113177-5^11317788069Jean-Louis Charton01/2009
98841316^28233+28233^131688066Norbert Schneider07/2020
9885(2^292543+2234)/288064Stefano Morozzi01/2020
9886(10^88020+101)/388020Robert Price04/2016
988752^51285-5188006Norbert Schneider09/2018
988821002^15501+15501^2100288006Hans Havermann08/2020
988920466^19951+19951^2046688004Hans Havermann08/2020
9890(2^292324+2346)/287998Stefano Morozzi01/2020
989121634^11683+11683^2163487998Hans Havermann08/2020
9892(6340^23143-1)/633987988Serge Batalov08/2020
989320674^18013+18013^2067487980Hans Havermann08/2020
9894(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
9895(11*10^87960-41)/387961Robert Price12/2021
9896(424*10^87930-1)/987932Robert Price11/2017
9897(2^292100+3070)/287931Stefano Morozzi01/2020
9898p(18225)#/2+12887929Robert Price04/2017
9899(10607^21841-1)/1060687919Serge Batalov08/2020
9900(2^292047+1550)/287915Stefano Morozzi01/2020
99014*6^112977+787914Lelio R Paula10/2014
9902(2^292016+1062)/287906Stefano Morozzi01/2020
9903(11359^21673-1)/1135887888Serge Batalov08/2020
990414^76677+6987882Lelio R Paula11/2015
9905(22*10^87863-1)/387864Robert Price12/2014
99062^291822-279781187848Enzo Doria04/2016
9907(22*10^87821-43)/387822Robert Price10/2021
9908(2^291730+1614)/287820Stefano Morozzi01/2020
9909(277*10^87817-7)/987819Robert Price02/2022
99102^291716-11138987816Enzo Doria05/2014
9911(782*10^87809-71)/987811Robert Price06/2017
99123^184039+182087809Lelio R Paula12/2015
991312^81356+4187798Lelio R Paula11/2015
991421307^13188+13188^2130787789Hans Havermann08/2020
9915(2527^25801-1)/252687788Serge Batalov08/2020
9916(2^291596+1986)/287779Stefano Morozzi01/2020
99186^112792-1898387770Enzo Doria03/2013
9917(3123^25117-1)/312287770Serge Batalov08/2020
99193*6^112787-587766Lelio R Paula10/2014
99207^103848+8287762Lelio R Paula10/2015
9921(19*2^291534-1)/17869639587754Lelio R Paula02/2014
9922(2^291506+918)/287752Stefano Morozzi01/2020
992324411^3932+3932^2441187749Hans Havermann08/2020
9924(3^183915+5)/12887748Lelio R Paula01/2013
992519^68619+2487747Lelio R Paula12/2015
99272^291480+118587745Lelio R Paula10/2013
99262^291482+186736987745Enzo Doria03/2016
99282^291467-93787741Yves Minet05/2013
9929(25*10^87726+161)/387727Robert Price01/2017
993011^84239-285087726Enzo Doria12/2012
993110^87720+21554187721Patrick De Geest01/2011
993210^87720-387720Markus Tervooren07/2010
9933(2^291383+3078)/287715Stefano Morozzi01/2020
9935(5*10^87712-473)/987712Robert Price12/2017
9934(2^291373+2946)/287712Stefano Morozzi01/2020
993622591^7630+7630^2259187711Hans Havermann08/2020
993722081^9378+9378^2208187709Hans Havermann08/2020
9938(2^291357+5)/684787704Lelio R Paula01/2013
9939(2^291280+462)/287684Stefano Morozzi01/2020
994020749^16816+16816^2074987680Hans Havermann08/2020
994193^44541-287679Lelio R Paula09/2013
99422^291261-10956187679Enzo Doria04/2014
9943(4*10^87669+149)/987669Robert Price03/2017
99442^291217+425787666Lelio R Paula10/2013
994522748^7137+7137^2274887660Hans Havermann08/2020
99462*12^81214-5^8121487645Mike Oakes12/2010
9947(2^291150+2291)/1587644Eric Chen08/2022
9948(85*10^87637-139)/987638Robert Price08/2021
9949(5005^23689-1)/500487632Serge Batalov08/2020
9950(5*10^87622-473)/987622Robert Price12/2017
995112^81188+8587617Lelio R Paula11/2015
9952(2^291030+3462)/287609Stefano Morozzi01/2020
9953(21*2^290980-1)/587595Lelio R Paula02/2014
9954(2^290980+1150)/287594Stefano Morozzi01/2020
99552^290958+12787588Lelio R Paula09/2012
995678531!4-887580Robert Price11/2019
99572^290923-6787577Lelio R Paula09/2012
99583*10^87573-9787574Robert Price08/2017
9959(13*10^87565+11)/387566Robert Price05/2015
9960(2^290881+1022)/287564Stefano Morozzi01/2020
9961(2^290857-7)/5587555Lelio R Paula01/2013
9962(2^290808+1498)/287542Stefano Morozzi01/2020
99632^290802+8287587541Lelio R Paula10/2013
9964(509203*2^290792-1)/756098787536Lelio R Paula04/2015
99653^183441+23687524Lelio R Paula12/2015
99664*10^87513-6987514Robert Price01/2022
99672^290618-3387485Lelio R Paula09/2012
9968(184*10^87473-1)/387475Robert Price02/2017
99692^290534-11515187460Enzo Doria06/2015
99702^290512-10975787453Enzo Doria04/2014
9971(32*10^87448-41)/987449Robert Price05/2015
9972(2^290493+3074)/287447Stefano Morozzi01/2020
9973(2^290491+9)/317987444Lelio R Paula01/2013
9974(25*2^290489-1)/5180987443Lelio R Paula02/2014
99752^290426+8287587427Lelio R Paula11/2013
99763*2^290415-787425Lelio R Paula08/2014
997810^87408+5787409Robert Price03/2011
99772^290366+7477987409Enzo Doria04/2016
997922284^8365+8365^2228487409Hans Havermann08/2020
998010^87408-12356987408Patrick De Geest07/2013
998121517^11536+11536^2151787404Hans Havermann08/2020
99826*10^87396+7787397Robert Price06/2020
9983(2^290268+3882)/287380Stefano Morozzi01/2020
99842^290265+5890587379Lelio R Paula10/2013
99857^103391+1687376Lelio R Paula10/2015
9986(115*10^87368-7)/987370Robert Price11/2017
9987(92^44491-1)/9187369Paul Bourdelais08/2017
99888*7^103379+387367Lelio R Paula10/2014
9989(2^290226+7)/7187365Lelio R Paula01/2013
9990(29*10^87355-89)/387356Robert Price01/2022
9991(3216^24907-1)/321587354Serge Batalov08/2020
9992(2^290160+2686)/287347Stefano Morozzi01/2020
999313^78407-3087341Lelio R Paula11/2015
99944*10^87337-9987338Robert Price12/2016
99957*10^87319+3987320Robert Price07/2016
99963*5^124921+287317Lelio R Paula10/2014
999778315!4-1687316Robert Price11/2019
99983^182984+8887306Lelio R Paula12/2015
9999(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
10000(10^87323-1)/30518336337576143505387303Anonymous10/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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